Superspace formulation of higher-derivative actions from D-branes

Higher-derivative operators play a fundamental role in the development of effective field theories. This thesis deals with the study of such operators in the context of the effective low-energy theory of type IIB superstring theory. In particular, we revisit a past attempt to find the supersymmetric form of the higher-derivatives for the D7-brane modulus in an orbifold compactification at the level of a globally supersymmetric theory. These higher-derivatives descend from the Dirac-Born-Infeld action of the D7-brane. Starting from the component Lagrangian the task is to identify the supersymmetric higher-derivative operator which reproduces the component terms. To this end, we develop a new systematic approach to determine this supersymmetric form and test it for the present example.